Search results
Results from the WOW.Com Content Network
The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
Knowing that some Catalan number counts the number of triangulations of a polygon is part of the excitement of what mathematics is all about. Knowing which Catalan number it is, through the mnemonic that "the n-th Catalan number counts the case of n triangles" is intended to be the frosting on the cake. I'd like to put in the count of triangles ...
Catalan numbers, a sequence of natural numbers that occur in various counting problems Catalan solids , a family of polyhedra Catalan's constant , a number that occurs in estimates in combinatorics
Eugène Charles Catalan (French pronunciation: [øʒɛn ʃaʁl katalɑ̃]; 30 May 1814 – 14 February 1894) [2] was a French and Belgian mathematician who worked on continued fractions, descriptive geometry, number theory and combinatorics.
132 is the sixth Catalan number. [1] With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136. [2]132 is an oblong number, as the product of 11 and 12 [3] whose sum instead yields the 9th prime number 23; [4] on the other hand, 132 is the 99th composite number.
Lobb numbers form a natural generalization of the Catalan numbers, which count the complete strings of balanced parentheses of a given length. Thus, the nth Catalan number equals the Lobb number L 0,n. [2] They are named after Andrew Lobb, who used them to give a simple inductive proof of the formula for the n th Catalan number. [3]
In some publications this equation is sometimes referred to as Two-parameter Fuss–Catalan numbers or Raney numbers. The implication is the single-parameter Fuss-Catalan numbers are when r = 1 {\displaystyle \,r=1\,} and p = 2 {\displaystyle \,p=2\,} .
Catalan (català) is a Western Romance language.It is the official language of Andorra, [2] and an official language of three autonomous communities in eastern Spain: Catalonia, the Balearic Islands and the Valencian Community, where it is called Valencian (valencià).